To "accost" someone is to approach them and talk to then in an intense, demanding way. The demand can be anything. For example, "the homeless man accosted me and asked me for money." The word has a specific unpleasant connotation. It is a word that is often chosen when the "demand" is for sex.

It means to confront someone to tell them off. For example a teacher could “accost” a pupil in the corridor for wearing the wrong uniform. It means to go up to someone and shout at them or talk sternly to them when you think they are doing something wrong (normally confrontational or not in a very polite way). It’s not a word that is often used in daily speech, it sounds more bookish and formal to me.